Lens with off-axis curvature center

ABSTRACT

An off-axis curvature center lens is characterized by an x-y-z coordinate system of the convergence-reducing lens, the off-axis curvature lens comprising a distance-vision region with a non-negative distance-vision optical power, having a front distance-vision surface with a center of front distance-vision curvature, and a rear distance-vision surface with a center of rear distance-vision curvature; and a near-vision region with an optical power within 0.5D of the distance-vision optical power, having a front near-vision surface with a center of front near-vision curvature, and a rear near-vision surface with a center of rear near-vision curvature; wherein at least one of an x-coordinate of the center of front near-vision curvature is nasal relative to an x-coordinate of the center of front distance-vision curvature, and an x-coordinate of the center of rear near-vision curvature is temporal relative to an x-coordinate of the center of rear distance-vision curvature.

FIELD OF INVENTION

This invention relates generally to improved spectacle lenses, in moredetail to spectacle lenses that reduce eye-strain and relax convergence,and alters proprioceptive feedback.

BACKGROUND

With normal vision, an individual is able to focus at objects located atdifferent distances. Ideally, an individual is able to focus on distantobjects, referred to as distance-vision, and on near objects, referredto as near-vision. The optical system of the eye uses numerous musclesto focus for both distance-vision and for near-vision. These musclesadjust various aspects of the eye when transitioning betweendistance-vision and near-vision. The muscle adjustments include makingsubtle changes to the shape of the crystalline lens to adjust the focusof the lens, rotating the eyeballs to rotate their optical axes, andchanging the size of the pupils.

Presbyopia is a natural deterioration of near vision caused by loss offlexibility in the eye's crystalline lenses as one ages. Presbyopia canbe partially compensated by wearing “reading” glasses that correct nearvision refraction errors so that the eye does not have to focus asstrongly when gazing at near objects. Presbyopic persons need differentoptical corrections for near-vision and for distance-vision. However,using two glasses and changing them with great frequency is distracting.To avoid continually exchanging eyeglasses, bifocals may be used thatoffer different optical corrections for near-vision and fordistance-vision. The transition between these two vision regions can beabrupt or gradual. The latter eyeglasses are called Progressive AdditionLenses (PALs). Abrupt change bifocals have a visible line separating thetwo vision regions, while PALs have no lines or edges visible betweenthe regions with different dioptric powers.

In spite of all this progress, some types of vision-related discomfortsstill persist. One of these discomforts is related to a shift of habitsin the modern, digital lifestyle. A large and increasing fraction ofprofessions require workers to spend a large and increasing fraction oftheir working time focusing at close-distance digital interfaces,including computer screens and mobile devices. The same is true for theprivate lives of many, spending hours playing video games, texting andchecking updates on cell phones, among others. All these professionaland behavioral shifts rapidly increased the time people spend looking atdigital screens, devices, displays, and monitors at a much closerdistance than before. The increased time of the eye being trained atnear-vision targets places excessive demands on the muscles involved innear-vision, often straining them beyond the comfort zone. This can leadto fatigue, discomfort, pain, or even digitally induced migraines. Up tonow, there is no widely accepted consensus on the precise causationmechanism of these digital-device related visual discomforts, pains andmigraines. Therefore, there is a need for glasses, or other optometricsolutions than can provide relief for digital eye discomforts.

SUMMARY

In some embodiments, a convergence-reducing lens is characterized by acentral normal of the convergence-reducing lens that defines a z-axis,and a central region of the convergence-reducing lens defines atangential, centered x-y plane, together defining an x-y-z coordinatesystem of the convergence-reducing lens, the convergence-reducing lenscomprising a distance-vision region with a non-negative distance-visionoptical power, having a front distance-vision surface with a center offront distance-vision curvature, and a rear distance-vision surface witha center of rear distance-vision curvature; and a near-vision regionwith an optical power within 0.5D of the distance-vision optical power,having a front near-vision surface with a center of front near-visioncurvature, and a rear near-vision surface with a center of rearnear-vision curvature; wherein at least one of an x-coordinate of thecenter of front near-vision curvature is nasal relative to anx-coordinate of the center of front distance-vision curvature, and anx-coordinate of the center of rear near-vision curvature is temporalrelative to an x-coordinate of the center of rear distance-visioncurvature.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-B illustrate the refraction angle of optical lenses.

FIGS. 2A-C illustrate the refraction angles of a monovision lens.

FIGS. 3A-B illustrate the induced refraction, increasing the gazeconvergence angle.

FIGS. 4A-B illustrate an effect of a convergence-reducing lens.

FIGS. 5A-D illustrate light propagation in convergence-reducing lenses.

FIGS. 6A-B illustrate embodiments of a convergence-reducing lens.

FIGS. 7A-D illustrate embodiments of a convergence-reducing lens.

FIGS. 8A-C illustrate contour-representations of variousconvergence-reducing lenses for near-zero optical powers.

FIGS. 9A-D illustrate contour-representations of variousconvergence-reducing lenses for optical power D.

FIGS. 10A-C illustrate various designs of the near-vision region.

FIGS. 11A-B illustrate lens designs.

FIGS. 12A-B illustrate off-axis centers of curvatures in variousembodiments of the convergence-reducing lens.

DETAILED DESCRIPTION

Embodiments of the invention are placed into context by first describinghow regular, positive power lenses of existing spectacles induceincreased gaze-convergence angles for near-vision, thus exacerbatingalready existing digital eyestrain. This will be followed by thedescription of the embodiments of the invention.

FIG. 1A illustrates how a typical, positive power mono-vision opticallens 1 effects incident light rays 2. When parallel rays 2 are incidenton the lens 1, the lens 1 focuses them into a focus point F.

FIG. 1B zooms in on an off-center, or off-axis portion of the incidentlight rays. Visibly, the off-center, or off-axis parallel rays arerefracted towards the focus point F by the angled front surface and theangled back surface of the lens 1 according to well-established laws oflight-refraction. The overall effect of the light rays propagatingthrough these two angled surfaces is that they get refracted by aninduced angle of refraction α.

There are different, related ways to characterize the amount ofrefraction by a lens region at a radial distance r from the axis. Onecharacterization is by the refraction angle α itself Another is by thetangent of this same refraction angle, expressed as a ratio of r, theradial distance of the region of the lens from a lens optical axis 3, tof, the focal distance of the lens:tan α=r/f.  (1)

This relation shows that a lens of optical power of D diopters, definedas D=1/f[1/m], induces a refraction angle α for rays that are incidentat the lens at a radial distance r from the axis 3 of the lens 1, whereα is given bytan α=r*D.  (2)

FIG. 2A illustrates a simple mono-vision lens 10 with optical power D.

FIG. 2B illustrates the above notion that the angled surfaces of themono-vision lens 10 of FIG. 2A induce a refraction angle α in regionsaway from the axis of the lens. Since the magnitude of the refractionangle α depends only on the radial distance from the axis, the iso-αcontours, i.e. the points where the magnitudes of the refraction angle αare equal, form concentric circles. The shown circles have radii ofabout r=0.8 mm, r=1.6 mm, 2.4 mm, r=3.2 mm, and r=4.0 mm. Equation (2)provides that tan α, the tangent of the refraction angle α is given asthe product of the radius r and the optical power D. Here, the units ofD are [1/m], and the units of r are [m]. Since typical values of r are1-20 millimeters, and values of D are a couple diopters [1/m], tan α istypically of the order of 10⁻³-10⁻² radian, which translates to afew-to-a-few-tens of arc-minutes. As an example, for r=1 mm, andD=1[1/m], tan α=1*10⁻³ radian=3.5 arc-minutes. At small angles, tan α iswell approximated by α. Therefore, returning to FIG. 2A, on the showncircles the deflection angle α takes the values 2.8D, 5.6D, 8.4D, 11.2Dand 14D, in arc minutes.

Finally the lower graph of FIG. 2B illustrates α^(x), the x-component ofthe refraction angle α, where the x-y coordinate system is based at thecenter of the lens 10, with its axes being horizontal and vertical inthe plane of the lens 10, as shown. There are several ways to defineα^(x) that are analogous to each other. One practical definition isα^(x)=sin ϕ*α, where ϕ is the angle measured from the negative, or lowerhalf of the y-axis, pointing straight down in the plane of FIG. 2B, asshown. Combining with Eq. (2), and using that sin ϕ* r=x, the xcoordinate of the radial vector of length r, one gets the simplerelation:α^(x) =x*D.  (3)

The lower graph in FIG. 2B shows α^(x) as a function of the angle ϕ ingeneral. The upper figure shows the particular values of α^(x) along the+45 degree and along the −45 degree lines, using sin(±45)=±0.7. Thesevalues are: α^(x)=±2D, ±4D, ±6D, ±8D and ±10D, as shown.

Analogous definitions of α^(x) include tan α^(x)=sin ϕ* tan α, whichaccounts more precisely for the geometry of projections of a refractedlight 2. However, for the present small angles these two definitionsyield very similar mathematical relations and numerical values. Finally,the formula can be extended for light rays 2 that are not parallel withthe optical axis 3, but, rather, make an angle with the optical axis 3.In general, such extensions would yield an object-angle dependentexpression, through a dependence on the angle β. Notably though, such aβ-dependent formula can be expanded in α. Such an expansion wouldreproduce Eq. (2) in leading order in α.

α^(x) characterizes the s-component of the refraction angle α that inturn determines how much a wearer of the spectacle need to turn her/hisgaze to concentrate on these light rays. The larger the α^(x) in aregion of the lens, the more the light 2 passing through this region isrefracted by the lens and the more a wearer has to turn her/his gaze.

FIG. 2C illustrates the iso-α^(x) contours for the lens 10 of FIG. 2B,where α^(x) assumes the same values. Visibly, for the mono-vision lens10 of optical power D, the iso-α^(x) contours are approximately straightlines parallel to the y-axis, since α^(x) only depends on the xcoordinate of the points of the contour. For larger optical powers andradii, where the linear approximations start to garner corrections, theiso-α^(x) contours start bulging radially outward close to the x-axis,

FIGS. 3A-B illustrate how the refraction angle, induced by a positivepower lens, impacts the convergence of the gaze of glass-wearers, basedon these general considerations.

FIG. 3A illustrates that when a person is gazing at a remote object,then the gazing-directions of the left and right eves are essentiallyparallel, and thus there is no convergence of the gazing-directions andthe eye muscles are not strained at all. In such cases, the two z-axes3, pointing to the remote object through the center of the eye 5,coincide with the two eye-optical axes 9. The light 2 from the remoteobject is entering the eye 5 through the eye-lens 7 on its way to hitthe retina of the eye 5. These parallel axes will be used as referencesto characterize the gaze-convergence angles of gazes directed at nearobjects through various lenses next.

FIG. 3B illustrates that when a person is gazing at a near object, thegazes of the left and right eyes are tilted, or rotated, towards eachother, each gaze making a non-zero gaze-convergence angle β with thez-axes 3. Since the gaze-convergence angle β characterizes theconvergence of the gazes of the two eyes towards each other, in whatfollows the gaze-convergence angle β will refer specifically to thex-component of the overall gaze-rotation angle of the eye. This makesthe gaze-convergence angle β analogous to the x-component of therefraction angle α^(x), while also simplifying the terminology.

As mentioned before, the eyeballs are rotated by muscles attachedexternally to the eye. In particular, the lateral, x-directional,rotations are controlled by the medial rectus and the lateral rectusmuscles, and the vertical rotations are controlled by the superiorrectus and the inferior rectus, and inferior oblique muscles. When themedial rectus muscles of the left-eye and the right-eye contract, thegazes of these eyes converge towards each other. A person, traininghis/her eye on a near object, such as an electronic screen, a digitalscreen, a screen of a mobile electronic device, work-related papers, oreven a book, for extended periods requires the continuous contraction ofthe medial rectus muscles, thus exerting substantial strain on them.This “digital eyestrain” can lead to fatigue, leading to headache,eventually culminating in migraines, caused by the demands of themodern, digital lifestyle.

The digital lifestyle can induce other forms of asthenopia, oreye-strain, and other types of convergence-disorders, includingproprioceptive disparity, and fixation disparity. Proprioceptivedisparity is an imbalance between where the eyes are consciously focusedand the nonvisual perception of where the object is located in space.This disparity often varies with space. The brain of a patient with aproprioceptive disparity can compensate this disparity to a degree inorder to maintain a clear image of the target. However, when thedisparity becomes too big to be compensated, the trigeminal nerve canget overstimulated, resulting in patients experiencing headaches, eyefatigue, pain around the eyes, blurred vision, neck pain, dry eyes, andother general symptoms of asthenopia.

A class of symptoms especially worthy of mentioning is Computer VisionSyndrome (CVS), which is estimated to affect more than 100 millionAmericans. Computer Vision Syndrome is the physical eye discomfort feltafter a prolonged amount of time in front of digital devices at near,causing an array of unnecessary symptoms, and can have effects onproductivity.

Another large class of symptoms is known by the name of Chronic DailyHeadaches (CDH). CDH symptoms are estimated to affect more than 30million Americans. These patients suffer from an over-stimulation of thetrigeminal nerve that manifests itself in the form of chronic dailyheadaches. Various factors and triggers are believed to contribute tothe debilitating issue of chronic daily headache. As a result, patientssuffering from CDH are limited to treatment options that merely seek todull the symptoms. A large subset of chronic daily headache patients(believed to be as large as 33% of the population) shows objective signsof a misalignment between how the central visual system, peripheralvisual system and neurological system interact.

FIG. 4A illustrates that positive power spectacles 10′ can exacerbatethe symptoms of eye-strain, astenophia, Computer Vision Syndrome andproprioceptive disparity, caused by digital devices, because looking atdigital devices, or objects 11 that are nearby forces the wearer to gazethrough the lower-inferior nasal quadrant, the “near-vision” region, oftheir glasses. As shown before, in this off-center near-vision regionpositive power lenses 10 refract the light by a refraction angle α, asdescribed by Eqs. (1)-(3). A ray that propagates front the near object11 to the retina with the refraction angle a forces on the wearer agreater gaze-convergence angle β than a ray that propagates from thesame object to the same retina but without the refraction angle α.Therefore, positive power lenses 10 force an increased gaze-convergenceangle β and thus cause an increased strain on the medial rectus muscleswhen the wearer is looking at near objects. The sustained and excessivecontraction of the medial rectus muscles increases the tendencies for adigital migraine that affect and possibly debilitate the wearer.

FIG. 4B illustrates embodiments of a convergence-reducing lens 100 in aconvergence-reducing spectacle 100′ that can reduce, and often eliminatethe symptoms caused by eye-strain, astenophia, Computer Vision Syndromeand proprioceptive disparity. The convergence-reducing spectacles 100′with convergence-reducing lenses 100 have a suitably modifiedrefraction-angle α that reduces the gaze-convergence angle β when theirwearers look at a nearby object, such as at a digital device. Reducedgaze-convergence angles β require a lesser rotation of the eyes in thenasal direction, and therefore relieve the continuous contraction andstrain of the medial rectus muscles of the eyes. This reduced musclestrain reduces and often eliminates digital migraines.

FIGS. 5A-B illustrate in detail an embodiment of an eye-strain-reducinglens 100, or convergence-reducing lens 100 that relieves eye-strain andrelated digital eye discomforts. Throughout this application, the termseye-strain-reducing lens and convergence-reducing lens will be used andtreated interchangeably. For clarity, only one of theconvergence-reducing lenses 100 of the convergence-reducing spectacle100′ are shown. The below description applies for the other lens of theconvergence-reducing spectacle 100′ with the appropriate modifications.A nose of the spectacle-wearer is shown for reference. Embodiments ofthe convergence-reducing lens 100 can define an x-y-z coordinate systemas follows. A central normal of the convergence-reducing lens 100 candefine a z-axis 3, and a central region of the convergence-reducing lens100 can define a tangential, centered x-y plane. The center of thecoordinate system can be at the center of the lens 100. The conventionis adopted that the x-axis is “horizontal” with respect to the spectacle100′, and thus goes through the centers of both the left and the rightconvergence-reducing lenses 100. Accordingly, the y-axis is vertical.

With this coordinate system, and with further reference to FIG. 8A, theconvergence-reducing lens 100 can include a distance-vision region 110,having a non-negative distance-vision optical power, configured torefract a light ray 2, directed by a source 11 at a distance-visionregion point P_(d) at a distance-vision x-distance x_(Pd) from a centerof the coordinate system, to propagate to an eye-center representativelocation 8. In some embodiments, the eye-center representative location8 can be an eye center 8 itself. In other embodiments, it can be asensor, positioned at the location 8, or a screen, positioned acrosslocation 8, wherein the eye-center representative location 8 lies on thez-axis 3, at a z-distance in the range of 15-25 mm from the center ofthe lens's coordinate system in a direction that is opposite to thedirection of the source. These latter eye-center representativelocations 8 can be more suitable and accessible for measurements andcharacterizations.

The convergence-reducing lens 100 can further include a near-visionregion 120, having a near-vision optical power that matches thedistance-vision optical power within 0.5 diopters D, configured torefract a light ray 2, directed by the source 11 at a near-vision regionpoint P_(n) at a near-vision x-distance x_(Pn) from the center of thecoordinate system, to propagate to the eye-center representativelocation 8. Since the optical power of the near-vision region 120 can bevery close, and in some embodiments, equal to the optical power of thedistance-vision region 110, embodiments of the convenience-reducing lens100 can be called a mono-vision lens, or a single-vision lens. Thisaspect can distinguish these lenses from other, traditional bi-focallenses where the near-vision and distance-vision optical powers aredifferent.

For clarity, in this document the term “optical power” refers to theoptical power specifically related to the focal length f of the lens,and is measured in diopters D that are inversely related to the focallength: D=l/f. Also, FIG. 5A can be a cross section of theconvergence-reducing lens 100 at a high, positive y coordinate, whereasFIG. 5B may illustrate a cross section of the same convergence reducinglens 100 at a lower, negative y coordinate.

In embodiments, the near-vision x-distance x_(Pn) is smaller than thedistance-vision x-distance x_(Pd), as shown. Visibly, since in theseembodiments the near-vision x-distance x_(Pn) is smaller than thedistance-vision x-distance x_(Pd), the wearer of thisconvergence-reducing lens 100 can rotate an eye-optical axis 9 ofhis/her eye closer toward the z-axis 3 when looking at the source 11through the near-vision region 120 relative to the case when the weareris looking at the same source 11 through the distance-vision region 110,thereby reducing the gaze convergence angle, as described further next.As indicated in FIG. 5B, the reduced gaze-convergence angle β translatesinto a stress-reducing rotation of the eye 5. Accordingly, theconvergence-reducing lens 100 can also be called an eye-strain reducinglens 100. For this reason, the convergence-reducing spectacles 100′deliver the much-needed medical benefit of reducing eye-strain, digitalmigraines, proprioceptive disparity, fixation disparity, asthenopia, andconvergence-disorders in general.

A first inventive layer of the described technologies involves bifocalglasses, which already have a near-vision region separate from the usualdistance-vision region. Such glasses can be bestowed with the additionalmedical benefit of eye-strain reduction by making the convergenceproperties of these two vision regions also different.

Beyond this layer, a distinguishing feature of the here-describedsingle-vision, or monovision convergence-reducing lenses 100 is thatthey have a near-vision region 120 with a refractive power differentfrom the refractive power of the distance-vision region 110, in spite ofthe two regions having matching optical powers. This is to be contrastedwith bifocal lenses, where both the. refractive and the optical powersof the two vision regions are different. This is a qualitative, crucialdistinction for at least the following reasons.

(1) Bifocal spectacles already have two vision regions with a differingoptical property, the optical power. Therefore, it may occur to a lensdesigner to make a further optical property also different, such as therefractive power, to reduce convergence. However, in monovision lensesit is far from obvious for a designer to think of and to create anear-vision region for the sole purpose of delivering a differentrefractive power, while making sure that the near-vision region retainsthe same optical power as the rest of the lens.

(2) The global market for spectacle lenses exceeded 1 billion units soldworldwide in 2015, and more than 320 million in the US alone. It is alsoestimated that 75% of the US population, or about 240 million peoplewear some sort of vision correcting spectacles. By far the broadestmarket segment of spectacles sold in the US today, about 90% of thetotal market, have single vision lenses, and only about 10%, or 20-25million people wear bifocals. The mostly younger and early-middle agewearers of single-vision tenses simply do not need bifocal lenses. Someindustry surveys estimate the number of people who suffer, or report,Computer Vision Syndrome to exceed 100 million people. Therefore,introducing convergence-reducing near-vision regions into single visionspectacles will extend the reach of the convergence-reduction technologyfrom the narrow, 10-20 million unit/year market segment of bifocals tothe 100 million-plus unit/year market segment of monovision glasses.Therefore, the here-described monovision glasses will dramaticallybroaden the group of people to whom the medical benefit ofconvergence-reduction can be delivered.

(3) Convergence-reducing monovision glasses with zero or near zerooptical powers will qualitatively broaden the market penetration to yetanother wide class. These glasses will deliver the medical benefit ofconvergence reduction to people who do not need optical power correctionand therefore did not think of wearing glasses up to now. For thisreason, zero optical power monovision spectacles will dramaticallyextend the segment of the population to whom the medical benefit ofconvergence-reduction is delivered even further.

Finally, it is mentioned that in present-day optometric practice, mostdoctors have a different theory of the cause of eye-strain, andtherefore offer very different treatments and procedures to alleviateeye-strain, or asthenopia. Optometrists often prescribe switching toglasses with blue light filters, or suggest using humidifiers.Therefore, prescribing glasses with the here-describedconvergence-reduction technology rests on a very different medicalinsight regarding what causes eye-strain, and an inventive treatment toalleviate it that is genuinely different from what is prescribed bytoday's optometric practitioners.

Here and later in the text, the light propagation is described asoriginating by the source 11, or from an object 11, interchangeably. Thesource 11 can be a laser pointer or other directed light source thatactively generates a light ray 2. In some other embodiments, the object11 may not be an active light source, rather, an object or mirror thatreflects a light in the described direction, wherein the lightoriginated somewhere else. From the viewpoint of the light propagation,these two cases can be interchangeable. The object 11, or source 11, canbe at a z-distance z_(o/s) from the x-y plane of theconvergence-reducing lens 100.

In embodiments of the convergence-reducing lens 100, the distance-visionregion 110 can be configured to refract the light ray 2, directed by thesource 11, or object, 11 at the distance-vision region point P_(d) atthe distance-vision x-distance x_(Pd), to intersect a y-z plane of thecoordinate system with a distance-vision gaze-convergence angle β_(d);whereas the near-vision region 120 can be configured to refract thelight ray 2, directed by the source 11 at the near-vision region pointP_(n) at the near-vision x-distance x_(Pn), to intersect the y-z planewith a near-vision gaze-convergence angle β_(n). In these embodiments ofthe convergence-reducing lens 100 the near-vision gaze-convergence angleβ_(n) can be smaller than the distance-vision gaze-convergence angleβ_(d). Typically, the intersection of the refracted light 2 with the y-zplane with the gaze convergence angle β_(n/d) occurs at the eye-centerrepresentative location 8.

Here, the gaze-convergence angles β_(d) and β_(n) characterize theconvergence of the left and right eye's gaze, and thus they cancorrespond to the x-component of the overall, 3d dimensional rotationangle of the eyes, in analogy to α^(x), the x-component of the overallrefraction angle α.

This is a second expression that when the wearer looks at an object 11through the near-vision region 120 of the convergence-reducing lens 100,she/he does not need to rotate her/his eyes away from the z-axis 3 asmuch as in the case of looking at the same object through thedistance-vision region 110 of the lens 100. Therefore, embodiments ofthe convergence-reducing lens 100 indeed reduce the convergence angle βof the gaze of its wearer, when looking at objects through thenear-vision region 120, compared to looking through the distance-visionregion 110, or even through an analogous regular positive power lens 10.

In some embodiments of the convergence-reducing lens 100, thedistance-vision region 110 can be configured to refract the light ray 2,directed by or from the source 11 at the distance-vision region pointP_(d) at the distance-vision x-distance x_(Pd), by a distance-visionrefraction angle α_(d), whereas the near-vision region 120 can beconfigured to refract the light ray 2, directed by or from the source 11at the near-vision region point at the near-vision x-distance x_(Pn), bya near-vision refraction angle α_(n). In such embodiments of theconvergence-reducing lens 100, an x-component α_(n) ^(x) of thenear-vision refraction angle α_(n) can be smaller than an x-componentα_(d) ^(x) of the distance-vision refraction angle α_(d). This is athird expression that the lens 100 is reducing the gaze-convergence βwhen its wearer is looking at the object 11 through the near-visionregion 120, relative to looking at the same object 11 through thedistance-vision region 110.

The above three expressions of the gaze-convergence reducing aspects ofthe convergence-reducing lens 100 are stated as boxed inequalities inFIG. 5B. These inequalities are repeated here:x_(Pn)<x_(Pd),  (4)β_(n)<β_(d), and  (5)α_(n) ^(x)<α_(d) ^(x).  (6)

Embodiments of the convergence-reducing lens 100 satisfy at least one ofthese three inequalities (4)-(6).

The above descriptions of embodiments of the convergence-reducing lens100 also articulate auditing protocols to determine whether a lens is aconvergence-reducing lens. (1) It is possible to measure the describeddistances x_(Pd) and angles α_(d) ^(x) and β_(d) directly when a wearerof the lens is looking at an object through a potential distance-visionregion of a lens, followed by measuring the corresponding distances andangles α_(n) ^(x) and β_(n) as the wearer looks thiough a potentialnear-vision region of the lens, and then to compare the measured anglesand distances to verify whether they satisfy at least one of thedescribed three inequalities. For potential lenses, where the changes ofthe angles are small, an eye-tracking or eye-imaging system can be usedto determine the changes in the wearer's gaze-angle to detect the smallchanges and differences. (2) Instead of measuring angles and directionsof a wearer's gaze, an eye model with realistic parameters can be usedas well. The eye model can include a disk of a diameter of about 20-25mm, such as 24 mm, rotatable around a y-axis at an eye-centerrepresentative location 8. The front of the eye model can be, positioned10-15 mm behind the lens 100, the eye-center representative location 8about 20-30 mm behind the lens 100. The eye model can include anappropriate eye lens 7, with a total optical power approximately equalto that of the cornea, about 40-45 D, plus that of the lens, about 15-25D. A directed light source, such as a laser pointer or equivalents canbe deployed in place of the source 11 and its light can be pointed atthe potential distance-vision region and near-vision region of anaudited lens so that after refraction by the lens the light goes throughthe eye-center representative location 8 of the eye model in both cases.The described angles and distances can then be measured to determinewhether at least one of the three above inequalities applies.

(3) Finally, measurements without involving a wearer's eye, or even aneye-model, can also be sufficient to determine whether a lens is anembodiment of the convergence-reducing lens 100. A lens can be auditedon a fixed optical table by pointing a laser pointer from a position ofthe source 11 at the lens such that its light after refraction by thelens propagates through a candidate point for an eye-centerrepresentative location 8, about 20-30 mm behind the center of the lens100 along the z-axis 3. The light's propagation can be tracked, e.g., byimplementing a screen in the y-z plane of the lens 100 on the sideopposite to the source 11. The light of the laser pointer 11 can bedirected at a potential distance-vision region of the audited lens andthrough a potential near-vision region of the audited lens, ensuringthat the refracted light in both cases intersects the y-z plane at thesame z-distance from a center of the coordinate system that isrepresentative of an eye center 8. As described above, suchrepresentative locations can be 20-30 mm behind the center of the lens,on the z-axis 3. Once the angles and distances, discussed before, aremeasured for the light directed at the potential distance-vision andthen the potential near-vision regions, a lens is an embodiment of theconvergence-reducing lens if at least one of the three inequalities inFIG. 5B, and discussed above in Eqs. (4)-(6), holds for the measuredangles and distances. Other auditing protocols will be described later,in relation to FIGS. 5C-D and FIGS. 7A-D.

FIGS. 5A-B illustrate that the object/source 11 can be a near object,located at a source x-distance from the z-axis 3 of the coordinatesystem that is larger than a radius of the convergence-reducing lens100, and at a source z-distance that is between 10 cm and 100 cm. Suchan off-center, off-axis source 11 can be a good representation of a nearobject, aligned with a nose of the spectacle wearer, as shown.

FIGS. 6A-B illustrate that in other embodiments, the object 11 can befarther away. For example, the source/object 11 can be located at asource x-distance from the z-axis 3 of the coordinate system that issmaller than a radius of the convergence-reducing lens 100; and at asource z-distance that is larger than 100 cm. A class of theseobjects/sources 11. can include light from a laser pointer, directed inparallel to the z-axis 3 at the near-vision region point P_(n) and thedistance-vision region point P_(d). Embodiments of theconvergence-reducing lens 100 satisfy at least one of three inequalitiesthat are the analogs of the three inequalities of FIGS. 5A-B, shown inthe three boxes of FIG. 6B. The locations of the sources 11 are somewhatdifferent in the embodiments of FIGS. 5A-B and FIGS. 6A-B, therefore thedistance and angle ranges where the two sets of inequalities aresatisfied may not be exactly equal. Nevertheless, the validity ranges ofthe inequalities largely overlap, and therefore, both sets ofinequalities are representations of embodiments of theconvergence-reducing lens 100.

FIGS. 5C-D illustrate further aspects of the convergence-reducing lenses100. The characterization of the embodiments of FIGS. 5C-D is largelyanalogous to that of FIGS. 5A-B, since the characterization is motivatedby the reversibility of the paths of propagating light rays 2. Toindicate that elements in FIGS. 5C-D are related to the elements in FIG.5A-B by path-reversal, corresponding labels are used, with an “r” added,where appropriate. With these introductory considerations, someembodiments of a convergence-reducing lens 100 can have adistance-vision region 110, having a non-negative distance-visionoptical power, that is configured to refract a light ray 2 directed by asource 8 r at a distance-vision region point P_(d), at a distance-visionx-distance X_(Pd) from the center of the coordinate system, to propagateto an image point 11 r, or object/source 11 r. The image point 11 r. insome sense the reverse-pair of the object/source 11 of the embodimentsin FIGS. 5A-B, can be located at a z-distance z_(l) from the x-y planeof the lens 100. The source 8 r, in some sense the reverse-pair of theeye-center representative location 8 of the embodiments in FIGS. 5A-B,can be located on the z-axis 3 at a source-z-distance z_(s) from acenter of the coordinate system.

This embodiment of the convergence-reducing lens 100 can further includea near-vision region 120, having a near-vision optical power thatmatches the distance-vision optical power within 0.5D, configured torefract a light ray 2 directed by the source 8 r, located at the samesource-z-distance z_(s) from a center of the coordinate system, at anear-vision region point P_(n) at a near-vision x-distance x_(Pn) fromthe center of the coordinate system to propagate to the same image point11 r. In these embodiments, the near-vision x-distance x_(Pn) can besmaller than the distance-vision x-distance x_(Pd), in analogy toinequality (4) of the embodiments of FIGS. 5A-B.

In some embodiments, the distance-vision region 110 can be configured sothat the source 8 r can direct the light ray 2 to propagate to the imagepoint 11 r via a refraction at the distance-vision region point P_(d) bydirecting the light ray 2 with a distance-vision gaze-convergence angleβ_(d) relative to a y-z plane of the coordinate system; and thenear-vision region 120 can be configured so that the source 8 r candirect the light ray 2 to propagate to the same image point 11 r via arefraction at the near-vision region point P_(n) by directing the lightray with a near-vision gaze-convergence angle β_(n) relative to the y-zplane of the coordinate system. In these embodiments, the near-visiongaze-convergence angle β_(n) can be smaller than the distance-visiongaze-convergence angle β_(d), in analogy to inequality (5) above.

In some embodiments, the distance-vision region 110 can be configured torefract the light ray 2, directed by the source 8 r at thedistance-vision region point P_(d) to propagate to the image point 11 r,by a distance-vision refraction angle α_(d). The near-vision region 120can be configured to refract the light ray 2, directed by the source 8 rat the near-vision region point P_(n) to propagate to the same imagepoint 11 r, by a near-vision refraction angle α_(n). In embodiments,α_(n) ^(x), the x-component of the near-vision refraction angle α_(n)can be smaller than α_(d) ^(x), the x-component of the distance-visionrefraction angle, α_(d), in analogy to inequality (6) above.

FIGS. 8A-E illustrate a frontal view of an embodiment of theconvergence-reducing lens 100, looking onto the x-y plane of the lensfrom the z-axis direction. FIG. 8A shows iso-dioptric contour lines ofthe optical power, whereas FIG. 8B shows iso-α^(x) refraction anglecontour lines of the convergence-reducing lens 100. In some embodimentsof the convergence-reducing lens 100, the distance-vision region 110 canhave a distance-vision optical power of D diopters. The near-visionregion 120 can have a near-vision optical power that matches thedistance-vision optical power within 0.5 D; and a channel region 115that can connect the distance-vision region 110 and the near-visionregion 120. In some embodiments, the near-vision optical power can matchthe distance-vision optical power within 0.25 D. Because of the closematching of the distance-vision optical power and the near-visionoptical power, such embodiments can be called mono-vision lenses,single-vision lenses, or mono-focal lenses. The channel region 115 canhave an optical power that matches the distance-vision optical power andthe near-vision optical power within 0.5 D. In designs, where thedistance-vision optical power and the near-vision optical power are thesame, the channel region optical power can also have this shared value.In designs, where the distance-vision optical power and the near-visionoptical power differ by a small amount, such as by less than 0.5 D, thechannel region optical power can smoothly interpolate between thesenear-equal optical powers.

As shown in FIG. 8A, in some embodiments, the distance-vision opticalpower and the near-vision optical power can be “near zero”, such as lessthan 0.5 D. In some embodiments, the distance-vision and the near-visionoptical power can be zero diopter, 0 D.

Such 0 D convergence-reducing lenses 100 can be used by persons who donot need a correction of the optical power of their eyes, yet still feela digitally caused strain on their eyes, a “digital eyestrain”, that iscaused by extended periods of gazing at near objects, such as digital,electronic, or computer screens. Such persons may decide to wearconvergence-reducing spectacles 100′ that reduce their digital eyestraineven if they do not need an optical power correction.

Embodiments of the convergence-reducing lens 100 can further include anasal transition region 135 n and a temporal transition region 135 t. Inthese regions, the optical power may deviate from 0 D for reasons thatare explained below.

In some embodiments, an area of the near-vision region 120 can be largerthan 5 mm². In some embodiments, the area of the near-vision region 120can be larger than 10 mm².

FIG. 8B illustrates that in some embodiments of the convergence-reducinglens 100 with near 0 D optical power, α_(d) ^(x), an x-component of thedistance-vision refraction angle α_(d) in the distance-vision region 110can be near 0 as well, because α_(d) itself is near zero, based on Eqs.(2)-(3) and recalling that the optical power is 0 D. In theseembodiments, α_(n) ^(x), an x-component of the near-vision refractionangle α_(n) in the near-vision region 120 can be positive. The magnitudeof the refraction angles α was discussed previously. In many embodimentsα^(x) can fall in the range of 0.5-50 arc minutes, in some embodimentsin the range of 1-10 arc minutes. In FIG. 8B, α_(n) ^(x)=+6 arc minutesin the near-vision region 120 as indicated by underlining, the value.

These values are to be taken at the same x-distances from the center ofthe coordinate system for the distance-vision region 110 and for thenear-vision region 120. This is shown by the near-vision region pointP_(n) being a reflection of the distance-vision region point P_(d)across the x-axis, and thus having the same x-distance from the centerof the coordinate system.

Finally, these lenses may include a progression region 130, at leastpartially between the distance-vision region 110 and the near-visionregion 120, wherein a light ray 2, directed from the source 11 at aprogression region point at a progression x-distance is refracted topropagate to the eye-center representative location 8, wherein theprogression x-distance is between the near-vision x-distance x_(Pn) andthe distance-vision x-distance x_(Pd). Such progression regions 130 arealso characterized by α_(p) ^(x), an x-component of a progressionrefraction angle α_(p) that progresses between the x-components of thedistance vision refraction angle α_(d) ^(x) and the near-visionrefraction angle α_(n) ^(x). In the shown example, α_(p) ^(x) progressesbetween α_(d) ^(x)=0 and α_(n) ^(x) arc minutes. It is noted that, atleast in some embodiments, the progression region 130 need not coincidewith the channel region 115 of FIG. 8A.

In FIG. 8A, the transition regions 135 n and 135 t can emerge for thefollowing reason. In general, transition regions like the nasaltransition region 135 n and temporal transition region 135 t are formedbetween the distance-vision region 110 and the near-vision region 120when their optical properties are different in some aspect. This opticalproperty can be their optical power, cylinder, or astigmatism. Thisdifference in optical properties can lead to undesirable opticaldistortions. The transition regions 135 n/t are designed to minimizethese distortions. In the presently described convergence-reducinglenses 100, the optical power of the distance-vision region 110 and thenear-vision region 120 can be close, or even the same.

These convergence-reducing lenses 100, however, have differentrefraction angles α_(d) and α_(n) in the corresponding distance-visionregion 110 and near-vision region 120. This difference may induceoptical distortions. For this reason, it may reduce the opticaldistortions in these lenses 100, driven by the difference of therefraction angles α_(d) and α_(n), to include the transition regions 135n/t, and the progression region 130 to smoothly interpolate between theα_(d) and the α_(n) refraction regions. FIG. 9A shows that in someembodiments, only a nasal transition region 135 n may suffice for thispurpose.

FIG. 8B shows that in some embodiments, the majority of the near-visionregion 120 can occupy the lower, or inferior nasal quadrant of the lens100. In some embodiments, the near-vision region 120 can extend to thelower temporal quadrant, as shown.

FIG. 8C shows that in some embodiments, the near-vision region 120 mayfill even the lower nasal quadrant only partially.

FIG. 9A shows a convergence-reducing lens 100 that has an optical powerD. FIGS. 9B-D show the iso-α^(x) contours for various embodiments of theconvergence-reducing lens 100 of FIG. 9A. As discussed in relation toFIG. 2C, in lenses with a fixed optical power, the iso-α^(x) contoursmay be vertical lines.

FIG. 9B illustrates an embodiment of lens 100 where the near-visionregion 120 fills out the lower nasal quadrant only partially. FIG. 9Cillustrates an embodiment of lens 100 where the near-vision region 120fills out the lower nasal quadrant fully. FIG. 9D illustrates anembodiment of the lens 100 where the near-vision region 120 fills outthe lower nasal quadrant and also extends into the lower temporalquadrant.

FIGS. 9B-D also illustrate that embodiments of the convergence-reducinglens 100 can compensate and reduce the refraction by the positiveoptical power distance-vision region 110 so well in the near-visionregion 120 that the negative x-component of the distance-visionrefraction angle α_(d) ^(x) can be compensated into a smaller-magnitudenegative α_(n) ^(x) in FIG. 9B, a zero α_(n) ^(x) in FIG. 9C, or eveninto an overcompensated, opposite sign, positive α_(n) ^(x) in FIG. 9D.Such an overcompensated case was already illustrated with the light raysof FIG. 4B, with a refraction angle of the opposite sign than in FIG.4A.

In the special case when the optical power of the distance-vision region110 is approximately zero, α_(d) ^(x) is accordingly small or zero. Insuch cases, the near-vision region can compensate a near-zerox-component of the distance-vision refraction angle α_(d) ^(x) into apositive α_(n) ^(x).

FIGS. 10A-C illustrate that the near-vision region 120 can havedifferent shapes, including an oval, a quadrant, a triangle, arectangle, an elongated region, a diagonal region, a channel or acorridor.

FIGS. 11A-B illustrate two, embodiments of the convergence-reducing lens100 that can achieve and deliver the above described properties of theconvergence-reducing lens 100, in particular, that show configurationsand designs of lenses 100 that satisfy at least one of the earlierdescribed three inequalities (4)-(6).

FIG. 11A illustrates that embodiments of the convergence-reducing lens100 can include a front surface 140 f, with a distance-visionfront-tangential 145 fd at an x-distance from the center of thecoordinate system, and a near-vision front-tangential 145 fn at the samex-distance; and further they can include a rear surface 140 r, with adistance-vision rear-tangential 145 rd at the same x-distance, and anear-vision rear-tangential 145 rn at the same x-distance. Thesetangentials 145 are indicated by dashed lines. The distance-visionfront-tangential 145 fd and the distance-vision rear-tangential 145 rdform a distance-vision surface convergence angle γ_(dvr), while thenear-vision front-tangential 145 fn and the near-vision rear-tangential145 rn make a near-vision surface convergence angle γ_(nvr). In FIG.11A, the front and rear surfaces 140 f and 140 r of the near-visionregion 120 are the indented surfaces close to the center of the lens100, and therefore the near-vision surface convergence angle γ_(nvr) issmaller than the distance-vision surface convergence angle γ_(dvr):γ_(nvr)<γ_(dvr).  (7)

This inequality is one way to design a convergence-reducing lens 100that achieves at least one of the three inequalities (4)-(6). Severaldesigns can be consistent with this inequality. In some cases, theinequality of the angles in Eq. (7) can be solely driven by one of thetangentials being different, and the tangential of the other surfacebeing the same for the front and rear, surfaces. In some cases, the lens100 can be a meniscus lens 100. It is also noted that these anglesγ_(nvr) and γ_(dvr) depend on the x-distance where the tangentials werefitted to the surfaces 140 r and 140 f: γ _(nvr)=γ_(nvr)(x) andγ_(dvr)=γ_(dvr)(x). The angles γ_(nvr)(x) and γ_(dvr)(x) are to bedetermined and compared at the same x-distances from the center.

FIG. 11B shows another lens design to create a lens 100 that achieves atleast one of the three inequalities (4)-(6) in another manner. In thisdesign:γ_(nvr)=γ_(dvr).  (8)

Instead of modifying the surface tangentials, in these embodiments thedistance-vision region 110 has a distance-vision z-axis; the near-visionregion 120 has a near-vision z-axis, and the near-vision z-axis isrotated, or twisted in a nasal direction relative to the distance-visionz-axis. The twist is illustrated from looking down on the lens from theyaxis direction. The distance-vision z-axis at the highest y levels ofthe lens 100 where the distance-vision region 120 is naturally located,can be essentially parallel to the overall lens z-axis 3. Progressingtowards lower y levels, where the near-vision region 120 is naturallylocated, the x-y plane of the lens is getting rotated so that the z-axisis rotated in the nasal direction. Two of the twisted cross sections areshown in FIG. 11B. The middle cross section may correspond to theprogression region 130, and the bottom, most twisted cross section cancorrespond to the near-vision region 120, with its twisted near-visionz-axis.

It is noted that a manufacturing process of the embodiment of FIG. 11Bmay be remarkably easy as the process may involve forming a lens withthe desired optical powers and then warming the lens until its materialsoftens to a degree that allows a twisting of the lens by the designedamount.

Next, the embodiments of FIGS. 7A-D will be described. FIG. 7A showsthat embodiments of the convergence-reducing lens 100 can include adistance-vision region 110, having a non-negative distance-visionoptical power, that is configured to refract a light ray 2, directedparallel to the z-axis 3 at a distance-vision region point P_(d) at anx-distance from a y-z plane of the coordinate system x_(Pd), tointersect the y-z-plane at a distance-vision intersection z-distancez_(Id). The convergence-reducing lens 100 can also include a near-visionregion 120, having a near-vision optical power that matches thedistance-vision optical power within 0.5 D, that is configured torefract a light ray 2, directed parallel to the z-axis 3 at anear-vision region point P_(n), at an x-distance x_(Pn) that is equal tothe distance-vision region point P_(d): x_(Pn)=x_(Pd), to intersect they-z-plane at a near-vision intersection z-distance z_(In) that isgreater than the distance-vision intersection z-distance:z_(In)>z_(Id).  (9)

In some embodiments of the convergence-reducing lens 100, thedistance-vision region 110 can be configured to refract the light ray 2,directed parallel to the z-axis 3 at the distance-vision region pointP_(d) at the x-distance x_(Pd), by a distance-vision refraction angleα_(d). The near-vision region 120 can be configured to refract the lightray 2, directed parallel to the z-axis 3 at the near-vision region pointP_(n) at the x-distance x_(Pn), by a near-vision refraction angle α_(n).In embodiments, α_(n) ^(x), an x-component of the near-vision refractionangle α_(n) can be smaller than α_(d) ^(x), an x-component of thedistance-vision refraction angle ad that corresponds to the samex-distance x_(Pn)=x_(Pd):α_(n) ^(x)<α_(d) ^(x).  (10)

In some embodiments of the convergence-reducing lens 100, thedistance-vision region 110 can be configured to refract the light ray 2,directed parallel to the z-axis 3 at the distance-vision region pointP_(d) at the x-distance x_(Pd), to intersect the y-z plane with adistance-vision gaze-convergence angle β_(d); the near-vision region 120can be configured to refract the light ray 2 directed parallel to thez-axis 3 at the near-vision region point P_(n) at the same x-distancex_(Pn)=x_(Pd), to intersect the y-z plane with a near-visiongaze-convergence angle β_(n). In embodiments, the near-visiongaze-convergence angle β_(n) can be smaller than the distance-visiongaze-convergence angle β_(d) that corresponds to the same x-distance:β_(n)<β_(d).  (11)

The inequalities (9)-(11) characterize the embodiments of FIGS. 7A-Bsimilarly to the inequalities (4)-(6) characterizing the embodiments ofFIGS. 5A-B and FIGS. 6A-B. Embodiments of the convergence-reducing lens100 satisfy at least one of the three inequalities (9)-(11).

As before, embodiments of the convergence-reducing lens 100 can furtherinclude a progression region 130, at least partially between thedistance-vision region 110 and the near-vision region 120, that isconfigured to refract a light ray 2, directed parallel to the z-axis 3at a progression region point P_(p) at the x-distance x_(Pp) that is thesame as of the distance-vision region point x_(Pp)=x_(Pn)=x_(Pd), tointersect the y-z-plane at a progression intersection z-distance z_(Ip)that is between the near-vision intersection z-distance z_(In) and thedistance-vision intersection z-distance z_(Id): z_(Id)<z_(Ip)<z_(In).

FIGS. 7C-D describe embodiments that are related to reversing the pathof the light rays 2 in the embodiments of FIGS. 7A-B, albeit with somenecessary adaptations. FIG. 7C illustrates that embodiments of theconvergence-reducing lens 100 can include a distance-vision region 110,having a non-negative distance-vision optical power, configured torefract a light ray 2, directed by a source 15 r at a distance-visionregion point P_(d) at an x-distance x_(Pd) from a y-z plane of thecoordinate system, to make a distance-vision light-convergence angle 6 dwith the y-z-plane, wherein the source 15 r is located on the z-axis 3at an intersection z-distance z_(Id) from a center of the coordinatesystem. The lens 100 can further include a near-vision region 120,having a near-vision optical power that matches the distance-visionoptical power within 0.5 D, that is configured to refract a light ray 2,directed by the source 15 r at a near-vision region point P_(n) at thesame x-distance x_(Pn) from the y-z plane of the coordinate system asthat of the distance-vision point P_(d): x_(Pn)=x_(Pd), to make anear-vision light-convergence angle α_(n) with the y-z-plane. Here thesource 15 r can be at the intersection z-distance z_(In) that is againthe same as the source 15 r for the distance-vision z_(Id):z_(In)=z_(Id). In such embodiments, α_(n) ^(x), an x-component of thenear-vision light-convergence angle α_(n) can be greater than α_(d)^(x), an x-component of the distance-vision light-convergence angleα_(d):α_(n) ^(x)>α_(d) ^(x).  (12)

In some embodiments of the lens 100, the distance-vision region 110 canbe configured to refract the light ray 2, directed by the source 15 r atthe distance-vision region point P_(d) at x_(Pd), the x-distance fromthe y-z plane of the coordinate system, by a distance-vision refractionangle α_(d). Further, the near-vision region 120 can be configured torefract a light ray 2, directed by the source 15 r at the near-visionregion point P_(n) at x_(Pn), the x-distance from the y-z plane of thecoordinate system, by a near-vision refraction angle α_(n). Inembodiments, α_(n) ^(x), an x-component of the near-vision refractionangle α_(n) can be smaller than α_(d) ^(x), an x-component of thedistance-vision refraction angle α_(d):α_(n) ^(x <α) _(d) ^(x).  (13)

Inequalities (12)-(13) characterize the embodiments of FIGS. 7C-Danalogously to inequalities (4)-(6) characterizing the embodiments ofFIGS. 5C-D, and inequalities (9)-(11) characterizing the embodiments ofFIGS. 7A-B.

Several additional characteristics of the embodiments of FIGS. 5A-D andFIGS. 6A-B were described earlier. These characteristics can also applyto, or combined with, the embodiments of FIGS. 7A-D.

FIGS. 12A-B show embodiments of an eye-strain reducing lens 100, orconvergence reducing lens 100. These embodiments can be characterizedvia a description of the curvatures of the lens surfaces and theoff-center locations of their corresponding centers of curvatures. Insome detail, embodiments of the eye-strain-reducing lens 100, orconvergence-reducing lens 100 can have a central normal of theconvergence-reducing lens that defines a z-axis 3. The z-axis 3 istypically also the z-axis of a distance-vision region 110. A centralregion of the convergence-reducing lens 100 can further define atangential, centered x-y plane. The z-axis 3 and the x-y plane togetherdefine an x-y-z coordinate system.

The convergence-reducing lens 100 can include the above mentioneddistance-vision region 110 with a non-negative distance-vision opticalpower, having a front distance-vision surface 140 df with a radius ofcurvature R_(df) and a center of front distance-vision curvatureCC_(df), and a rear distance-vision surface 140 dr with a radius ofcurvature R_(dr) and a center of rear distance-vision curvature CC_(dr).The lens 100 can further include a near-vision region 120 with anoptical power within 0.5D of the distance-vision optical power, having afront near-vision surface 140 nf with a radius of curvature R_(nf) and acenter of front near-vision curvature CC_(nf), and a rear near-visionsurface 140 nr with a radius of curvature R_(nr) and a center of rearnear-vision curvature CC_(nr); wherein an x-coordinate of the center offront near-vision curvature x(CC_(nf)) can be nasal relative to anx-coordinate of the center of front distance-vision curvaturex(CC_(df)), or an x-coordinate of the center of rear near-visioncurvature x(CC_(nr)) can be temporal relative to an x-coordinate of thecenter of rear distance-vision curvature x(CC_(dr)). Expressed the aboveattributes in inequalities, and using the directionality of the x-axis,such that points lying to the right, temporal direction have greater xcoordinates than points lying to the left, nasal direction, theseconditions can be written as:x(CC _(nf))<x(CC _(df)), or  (14)x(CC _(nr))>x(CC _(dr)).  (15)

In some typical embodiments, the CC_(df) front and CC_(dr) rear centersof curvature of the distance-vision surfaces 140 df and 140 dr can belocated on the z-axis 3 and therefore, their x coordinates can be zero.In formal terms, x(CC_(df))=x(CC_(dr))=0. In such embodiments, theconvergence-reducing lens 100 can be configured so that x(CC_(nf)), thex-coordinate of the center of front near-vision curvature CC_(nf), isnasal relative to the z-axis 3 of the coordinate system, i.e.:x(CC _(nf))<0, or  (16)

x(CC_(nr)), the x-coordinate of the center of rear near-vision curvatureis temporal relative to the z-axis 3 of the coordinate system, i.e.x(CC _(m))>0.  (17)

In this sense, embodiments of the convergence-reducing lens 100 areoff-axis center of curvature lenses.

The above-described coordinates and x-distances of the centers ofcurvature x(CC_(nf)), x(CC_(nr)), x(CC_(df)), and x(CC_(dr)) can bedetermined with specialized tools and devices, such as spherometers andlens profilometers.

Designs of the convergence-reducing lens 100 can achieve the opticalpower of the near-vision region 120 to match the optical power of thedistance-vision region 110 within 0.5 D because the optical power infirst approximation is given by the radii of curvature of the lens frontand rear surfaces: Optical power (distance-vision)=f(R_(df), R_(dr)),and Optical power (near-vision)=f(R_(nf), R_(nr)). In the thin lensapproximation, the optical power is proportional to f(R₁,R₂)=(n−1)(1/R₁−1/R₂). As long as f(R_(nf), R_(nr))=f(R_(df), R_(dr)),the optical powers in the two regions are matching in a leading orderapproximation.

However the above relations assume that the centers of curvatures are onthe main optical axis of the lens. So, designs of the lens 100 can beviewed as built on the recognition that it is possible to leave theoptical power of the near-vision region 120 essentially equal to that ofthe optical power of the distance-vision region 110 by not manipulatingthe radii of the corresponding curvatures, yet, to adjust and manipulatethe near-vision refraction angles relative to the distance-visionrefraction angles by moving the centers of curvature off the axis of thelens. More concisely, in designs of the lens 100 it is possible to makethe refraction angles of the near-vision region different from therefraction angles of the distance-vision region, while preserving thatthe optical power of the near-vision region matches the optical power ofthe distance-vision region. The refraction angles and the optical powersof these two regions are adjustable relatively independently from eachother.

Some embodiments of these convergence-reducing lenses 100 can be furthercharacterized as follows. With reference to FIG. 11A, the frontdistance-vision surface 140 df and the rear distance-vision surface 140dr, at an x-distance from a center of the coordinate system, can definea distance-vision surface convergence angle γ_(dvr); and the frontnear-vision surface 140 nf and the rear near-vision surface 140 nr atthe same x-distance from the center of the coordinate system can definea near-vision surface convergence angle γ_(nvr), wherein in embodimentsthe near-vision surface convergence angle is smaller than thedistance-vision surface convergence angle:γ_(nvr)<γ_(dvr).  (18)

The convergence-reducing, off-axis curvature center lenses 100 can befurther characterized by, and combined with, the features described inrelation to FIGS. 1-11.

While this document contains many specifics, these should not beconstrued as Limitations on the scope of an invention or of what may beclaimed, but rather as descriptions of features specific to particularembodiments of the invention. Certain features that are described inthis document in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable subcombination. Moreover, although features may be describedabove as acting in certain combinations and even initially claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a subcombination or a variation of a subcombination.

The invention claimed is:
 1. A convergence-reducing lens, wherein: acentral normal of the convergence-reducing lens defines a z-axis, and acentral region of the convergence-reducing lens defines a tangential,centered x-y plane, together defining an x-y-z coordinate system of theconvergence-reducing lens, the convergence-reducing lens comprising adistance-vision region with a non-negative distance-vision opticalpower, having a front distance-vision surface with a center of frontdistance-vision curvature, and a rear distance-vision surface with acenter of rear distance-vision curvature; and a near-vision region withan optical power within 0.5D of the distance-vision optical power,having a front near-vision surface with a center of front near-visioncurvature, and a rear near-vision surface with a center of rearnear-vision curvature; wherein at least one of an x-coordinate of thecenter of front near-vision curvature is nasal relative to anx-coordinate of the center of front distance-vision curvature, and anx-coordinate of the center of rear near-vision curvature is temporalrelative to an x-coordinate of the center of rear distance-visioncurvature; wherein the front distance-vision surface and the reardistance-vision surface at an x-distance from a center of the coordinatesystem define a distance-vision surface convergence angle; the frontnear-vision surface and the rear near-vision surface at the x-distancefrom the center of the coordinate system define a near-vision surfaceconvergence angle; and the near-vision surface convergence angle issmaller than the distance-vision surface convergence angle.
 2. Theconvergence-reducing lens of claim 1, wherein: the convergence-reducinglens is configured so that at least one of the x-coordinate of thecenter of front near-vision curvature is nasal relative to the z-axis ofthe coordinate system, and the x-coordinate of the center of rearnear-vision curvature is temporal relative to the z-axis of thecoordinate system.
 3. The convergence-reducing lens of claim 1, wherein:the near-vision region has an area larger than 5 mm².
 4. Theconvergence-reducing lens of claim 1, wherein: the near-vision regionhas an area larger than 10 mm².
 5. The convergence-reducing lens ofclaim 1, wherein: the near-vision optical power matches thedistance-vision optical power within 0.25 D.
 6. The convergence-reducinglens of claim 1, wherein: the distance-vision optical power and thenear-vision optical power are less than 0.5 D.
 7. Theconvergence-reducing lens of claim 6, wherein: the distance-visionoptical power and the near-vision optical power are 0 D.
 8. Theconvergence-reducing lens of claim 1, wherein: a majority of thenear-vision region is located in a lower-inferior nasal quadrant of theconvergence-reducing lens.
 9. The convergence-reducing lens of claim 1,comprising: a front surface, having a distance-vision front-tangentialat an x-distance from the center of the coordinate system, and anear-vision front-tangential at the same x-distance; and a rear surface,having a distance-vision rear-tangential at the same x-distance, and anear-vision rear-tangential at the same x-distance; wherein thedistance-vision front-tangential and the distance-vision rear-tangentialmake a distance-vision surface convergence angle, and the near-visionfront-tangential and the near-vision rear-tangential make a near-visionsurface convergence angle, wherein the near-vision surface convergenceangle is smaller than the distance-vision surface convergence angle. 10.The convergence-reducing lens of claim 1, wherein: the distance-visionregion has a distance-vision z-axis; the near-vision region has anear-vision z-axis, wherein the near-vision z-axis is rotated in a nasaldirection relative to the distance-vision z-axis.